30 ideas
| 8093 | Seek wisdom rather than truth; it is easier [Joubert] |
| Full Idea: To seek wisdom rather than truth. It is more within our grasp. | |
| From: Joseph Joubert (Notebooks [1800], 1797) | |
| A reaction: A nice challenge to the traditional goal of philosophy. The idea that we should 'seek truth' only seems to have emerged during the Reformation. The Greeks may well never have dreamed of such a thing. |
| 8095 | We must think with our entire body and soul [Joubert] |
| Full Idea: Everything we think must be thought with our entire being, body and soul. | |
| From: Joseph Joubert (Notebooks [1800], 1798) | |
| A reaction: Not just that thinking must be a whole-hearted activity, but that the very contents of our thinking will be better if it arises out of being a physical creature, and not just a disembodied reasoner. Maybe the bowels are not needed to analyse set theory. |
| 8107 | The love of certainty holds us back in metaphysics [Joubert] |
| Full Idea: What stops or holds us back in metaphysics is a love of certainty. | |
| From: Joseph Joubert (Notebooks [1800], 1814) | |
| A reaction: This is a prominent truth from the age of Descartes, but may have diminished in the twenty-first century. The very best metaphysicians (e.g. Aristotle and Lewis) always end in a trail of dots when things become unsure. |
| 8099 | The truths of reason instruct, but they do not illuminate [Joubert] |
| Full Idea: There are truths that instruct, perhaps, but they do not illuminate. In this class are all the truths of reasoning. | |
| From: Joseph Joubert (Notebooks [1800], 1800) | |
| A reaction: A rather romantic view, which strikes me as false. An inspiring truth can suddenly collapse when you see why it must be false. Equally a line of reasoning can lead to a truth which need becomes an illumination. |
| 8098 | Truth consists of having the same idea about something that God has [Joubert] |
| Full Idea: Truth consists of having the same idea about something that God has. | |
| From: Joseph Joubert (Notebooks [1800], 1800) | |
| A reaction: Presumably sceptics about the existence of objective truth must also be sceptical about the possibility of such a God. I think Joubert is close to the nature of truth here. It is a remote and barely imaginable ideal. |
| 10702 | Set theory's three roles: taming the infinite, subject-matter of mathematics, and modes of reasoning [Potter] |
| Full Idea: Set theory has three roles: as a means of taming the infinite, as a supplier of the subject-matter of mathematics, and as a source of its modes of reasoning. | |
| From: Michael Potter (Set Theory and Its Philosophy [2004], Intro 1) | |
| A reaction: These all seem to be connected with mathematics, but there is also ontological interest in set theory. Potter emphasises that his second role does not entail a commitment to sets 'being' numbers. |
| 10713 | Usually the only reason given for accepting the empty set is convenience [Potter] |
| Full Idea: It is rare to find any direct reason given for believing that the empty set exists, except for variants of Dedekind's argument from convenience. | |
| From: Michael Potter (Set Theory and Its Philosophy [2004], 04.3) |
| 13044 | Infinity: There is at least one limit level [Potter] |
| Full Idea: Axiom of Infinity: There is at least one limit level. | |
| From: Michael Potter (Set Theory and Its Philosophy [2004], 04.9) | |
| A reaction: A 'limit ordinal' is one which has successors, but no predecessors. The axiom just says there is at least one infinity. |
| 10708 | Nowadays we derive our conception of collections from the dependence between them [Potter] |
| Full Idea: It is only quite recently that the idea has emerged of deriving our conception of collections from a relation of dependence between them. | |
| From: Michael Potter (Set Theory and Its Philosophy [2004], 03.2) | |
| A reaction: This is the 'iterative' view of sets, which he traces back to Gödel's 'What is Cantor's Continuum Problem?' |
| 13546 | The 'limitation of size' principles say whether properties collectivise depends on the number of objects [Potter] |
| Full Idea: We group under the heading 'limitation of size' those principles which classify properties as collectivizing or not according to how many objects there are with the property. | |
| From: Michael Potter (Set Theory and Its Philosophy [2004], 13.5) | |
| A reaction: The idea was floated by Cantor, toyed with by Russell (1906), and advocated by von Neumann. The thought is simply that paradoxes start to appear when sets become enormous. |
| 10707 | Mereology elides the distinction between the cards in a pack and the suits [Potter] |
| Full Idea: Mereology tends to elide the distinction between the cards in a pack and the suits. | |
| From: Michael Potter (Set Theory and Its Philosophy [2004], 02.1) | |
| A reaction: The example is a favourite of Frege's. Potter is giving a reason why mathematicians opted for set theory. I'm not clear, though, why a pack cannot have either 4 parts or 52 parts. Parts can 'fall under a concept' (such as 'legs'). I'm puzzled. |
| 10704 | We can formalize second-order formation rules, but not inference rules [Potter] |
| Full Idea: In second-order logic only the formation rules are completely formalizable, not the inference rules. | |
| From: Michael Potter (Set Theory and Its Philosophy [2004], 01.2) | |
| A reaction: He cites Gödel's First Incompleteness theorem for this. |
| 10703 | Supposing axioms (rather than accepting them) give truths, but they are conditional [Potter] |
| Full Idea: A 'supposition' axiomatic theory is as concerned with truth as a 'realist' one (with undefined terms), but the truths are conditional. Satisfying the axioms is satisfying the theorem. This is if-thenism, or implicationism, or eliminative structuralism. | |
| From: Michael Potter (Set Theory and Its Philosophy [2004], 01.1) | |
| A reaction: Aha! I had failed to make the connection between if-thenism and eliminative structuralism (of which I am rather fond). I think I am an if-thenist (not about all truth, but about provable truth). |
| 10712 | If set theory didn't found mathematics, it is still needed to count infinite sets [Potter] |
| Full Idea: Even if set theory's role as a foundation for mathematics turned out to be wholly illusory, it would earn its keep through the calculus it provides for counting infinite sets. | |
| From: Michael Potter (Set Theory and Its Philosophy [2004], 03.8) |
| 17882 | It is remarkable that all natural number arithmetic derives from just the Peano Axioms [Potter] |
| Full Idea: It is a remarkable fact that all the arithmetical properties of the natural numbers can be derived from such a small number of assumptions (as the Peano Axioms). | |
| From: Michael Potter (Set Theory and Its Philosophy [2004], 05.2) | |
| A reaction: If one were to defend essentialism about arithmetic, this would be grist to their mill. I'm just saying. |
| 13043 | A relation is a set consisting entirely of ordered pairs [Potter] |
| Full Idea: A set is called a 'relation' if every element of it is an ordered pair. | |
| From: Michael Potter (Set Theory and Its Philosophy [2004], 04.7) | |
| A reaction: This is the modern extensional view of relations. For 'to the left of', you just list all the things that are to the left, with the things they are to the left of. But just listing the ordered pairs won't necessarily reveal how they are related. |
| 13042 | If dependence is well-founded, with no infinite backward chains, this implies substances [Potter] |
| Full Idea: The argument that the relation of dependence is well-founded ...is a version of the classical arguments for substance. ..Any conceptual scheme which genuinely represents a world cannot contain infinite backward chains of meaning. | |
| From: Michael Potter (Set Theory and Its Philosophy [2004], 03.3) | |
| A reaction: Thus the iterative conception of set may imply a notion of substance, and Barwise's radical attempt to ditch the Axiom of Foundation (Idea 13039) was a radical attempt to get rid of 'substances'. Potter cites Wittgenstein as a fan of substances here. |
| 13041 | Collections have fixed members, but fusions can be carved in innumerable ways [Potter] |
| Full Idea: A collection has a determinate number of members, whereas a fusion may be carved up into parts in various equally valid (although perhaps not equally interesting) ways. | |
| From: Michael Potter (Set Theory and Its Philosophy [2004], 02.1) | |
| A reaction: This seems to sum up both the attraction and the weakness of mereology. If you doubt the natural identity of so-called 'objects', then maybe classical mereology is the way to go. |
| 10709 | Priority is a modality, arising from collections and members [Potter] |
| Full Idea: We must conclude that priority is a modality distinct from that of time or necessity, a modality arising in some way out of the manner in which a collection is constituted from its members. | |
| From: Michael Potter (Set Theory and Its Philosophy [2004], 03.3) | |
| A reaction: He is referring to the 'iterative' view of sets, and cites Aristotle 'Metaphysics' 1019a1-4 as background. |
| 8101 | To know is to see inside oneself [Joubert] |
| Full Idea: To know: it is to see inside oneself. | |
| From: Joseph Joubert (Notebooks [1800], 1800) | |
| A reaction: Extreme internalism about justification! Personally I am becoming convinced that 'know' (unlike 'believe' and 'true') is an entirely social concept. Fools spend a lot of time instrospecting; wise people ask around, and check in books. |
| 8094 | The imagination has made more discoveries than the eye [Joubert] |
| Full Idea: The imagination has made more discoveries than the eye. | |
| From: Joseph Joubert (Notebooks [1800], 1797) | |
| A reaction: As a fan of the imagination, I love this one. I suspect that imagination, which was marginalised by Descartes, is actually the single most important aspect of thought (in slugs as well as humans). Abstraction requires imagination. |
| 8103 | A thought is as real as a cannon ball [Joubert] |
| Full Idea: A thought is a thing as real as a cannon ball. | |
| From: Joseph Joubert (Notebooks [1800], 1801) | |
| A reaction: Nice. The realisation of a thought can strike someone as if they have been assaulted, and hearing some remarks can be as bad as being stabbed. That is quite apart from political consequences. Joubert is good on the physicality of thinking. |
| 8100 | Where does the bird's idea of a nest come from? [Joubert] |
| Full Idea: The idea of the nest in the bird's mind, where does it come from? | |
| From: Joseph Joubert (Notebooks [1800], 1800) | |
| A reaction: I think this is a very striking example in support of innate ideas. Most animal behaviour can be explained as responses to stimuli, but the bird seems to hold a model in its mind while it collects its materials. |
| 468 | Musical performance can reveal a range of virtues [Damon of Ath.] |
| Full Idea: In singing and playing the lyre, a boy will be likely to reveal not only courage and moderation, but also justice. | |
| From: Damon (fragments/reports [c.460 BCE], B4), quoted by (who?) - where? |
| 8096 | He gives his body up to pleasure, but not his soul [Joubert] |
| Full Idea: He gives his body up to pleasure, but not his soul. | |
| From: Joseph Joubert (Notebooks [1800], 1799) | |
| A reaction: A rather crucial distinction in the world of hedonism. There seems something sincere about someone who pursues pleasure body and soul, and something fractured about the pursuit of pleasure without real commitment. The split seems possible. |
| 8104 | What will you think of pleasures when you no longer enjoy them? [Joubert] |
| Full Idea: What will you think of pleasures when you no longer enjoy them? | |
| From: Joseph Joubert (Notebooks [1800], 1802) | |
| A reaction: A lovely test question for aspiring young hedonists! It doesn't follow at all that we will despise past pleasures. The judgement may be utilitarian - that we regret the pleasures that harmed others, but love the harmless ones. Shame is social. |
| 8097 | Virtue is hard if we are scorned; we need support [Joubert] |
| Full Idea: It would be difficult to be scorned and to live virtuously. We have need of support. | |
| From: Joseph Joubert (Notebooks [1800], 1800) | |
| A reaction: He seems to have hit on what I take to be one of the keys to Aristotle: that virtue is a social matter, requiring both upbringing and a healthy culture. But we can help to create that culture, as well as benefiting from it. |
| 8106 | In raising a child we must think of his old age [Joubert] |
| Full Idea: In raising a child we must think of his old age. | |
| From: Joseph Joubert (Notebooks [1800], 1809) | |
| A reaction: Very nice, and Aristotle would approve. If educators think much about the future, it rarely extends before the child's first job. We should be preparing good grand-parents, as well as parents and employees. Educate for retirement! |
| 8105 | We can't exactly conceive virtue without the idea of God [Joubert] |
| Full Idea: If we exclude the idea of God, it is impossible to have an exact idea of virtue. | |
| From: Joseph Joubert (Notebooks [1800], 1808) | |
| A reaction: I suspect that an 'exact' idea is impossible even with an idea of God. This is an interesting defence of the importance of God in moral thinking, but it only requires the concept of a supreme being, and not belief. |
| 8102 | We cannot speak against Christianity without anger, or speak for it without love [Joubert] |
| Full Idea: We cannot speak against Christianity without anger, or speak for it without love. | |
| From: Joseph Joubert (Notebooks [1800], 1801) | |
| A reaction: This seems to be rather true at the present time, when a wave of anti-religious books is sweeping through our culture. Presumably this remark used to be true of ancient paganism, but it died away. Christianity, though, is very personal. |